Exam 16: Mathematics Problems: Differential Equations and Linear Algebra

A particular solution of $\mathbf { X } ^ { \prime } = \left( \begin{array} { l l } 1 & - 2 \\1 & - 1\end{array} \right) \mathbf { X } + \left( \begin{array} { l } 2 \\t\end{array} \right)$ is

In the previous problem, the error in the classical Runge-Kutta method at $x = 0.1$ is (Hint: see the previous five problems.)

In the previous two problems, the error in the improved Euler method at $x = 0.1$ is

The solution of $y y ^ { \prime \prime } = \left( y ^ { \prime } \right) ^ { 2 }$ is

The differential equation $x d y - y d x = 0$ is Select all that apply.

A 2-pound weight is hung on a spring and stretches it 1/2 foot. The mass spring system is then put into motion in a medium offering a damping force numerically equal to the velocity. If the mass is pulled down 4 inches from equilibrium and released, the initial value problem describing the position, $x ( t )$ , of the mass at time $t$ is

Using power series methods, the solution of $2 x y ^ { \prime \prime } + y ^ { \prime } + 2 y = 0$ is

The solution of $y ^ { \prime \prime } + y = \tan x$ is